Math Problem Statement

The user submitted a query involving logarithmic expressions to be simplified using logarithmic properties, with exercises labeled 6, 7, and 8.

Solution

The image contains logarithmic equations that need to be solved using logarithmic properties.

Let's break down each exercise:

6. Gunakan sifat alogba=ba^{\log_b a} = b untuk menentukan hasil dari ekspresi berikut:

a. 100log5100_{\log_5} b. 32log832_{\log_8} c. 25log425_{\log_4} d. 4log834_{\log_8} - 3

Solution: This asks to use the property alogba=ba^{\log_b a} = b, simplifying each term.

  • (a) 100log5=52100_{\log_5} = 5^2
  • (b) 32log8=85/332_{\log_8} = 8^{5/3}
  • (c) (25_{\log_8 } etc out detailing() moving further..

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents
Logarithmic properties

Formulas

a^log_b(a) = b
log_b(x * y) = log_b(x) + log_b(y)
log_b(x / y) = log_b(x) - log_b(y)
log_b(x^n) = n * log_b(x)

Theorems

Logarithmic properties
Change of base theorem

Suitable Grade Level

Grades 10-12